{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 3, demo 5\n",
    "\n",
    "Bayesian Data Analysis, 3rd ed\n",
    "\n",
    "Demonstrate a normal model for the Newcomb's data (BDA3 p. 66)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import preliz as pz\n",
    "pz.style.use('preliz-doc')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# data\n",
    "data_path = os.path.abspath(\n",
    "    os.path.join(\n",
    "        os.path.pardir,\n",
    "        'utilities_and_data',\n",
    "        'light.txt'\n",
    "    )\n",
    ")\n",
    "y = np.loadtxt(data_path)\n",
    "# sufficient statistics\n",
    "n = len(y)\n",
    "s2 = np.var(y, ddof=1)  # ddof=1 -> sample estimate\n",
    "my = np.mean(y)\n",
    "\n",
    "# filtered data\n",
    "y_pos = y[y > 0]\n",
    "# sufficient statistics\n",
    "n_pos = len(y_pos)\n",
    "s2_pos = np.var(y_pos, ddof=1)\n",
    "my_pos = np.mean(y_pos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# for mu, compute the density in these points\n",
    "tl1 = [10, 40]\n",
    "t1 = np.linspace(tl1[0], tl1[1], 500)\n",
    "\n",
    "# compute the exact marginal density for mu\n",
    "pm_mu = pz.StudentT(n-1, my, np.sqrt(s2/n)).pdf(t1)\n",
    "\n",
    "# compute the exact marginal density for mu for the filtered data\n",
    "pm_mu_pos = (\n",
    "    pz.StudentT(n_pos-1, my_pos, np.sqrt(s2_pos/n_pos)).pdf(t1)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create figure\n",
    "fig, axes = plt.subplots(2, 1, sharex=True, figsize=(8, 8))\n",
    "\n",
    "# plot histogram\n",
    "ax = axes[0]\n",
    "ax.hist(y, np.arange(-44, 43, 2))\n",
    "# decorate\n",
    "ax.set_title('Newcomb\\'s measurements')\n",
    "ax.set_ylabel('count')\n",
    "ax.set_xlabel(r'$\\mu$')\n",
    "ax.tick_params(axis='x', reset=True, top=False)\n",
    "\n",
    "# plot the posterior of mu\n",
    "ax = axes[1]\n",
    "ax.plot(t1, pm_mu)\n",
    "# plot the posterior of mu in the filtered case\n",
    "ax.plot(t1, pm_mu_pos)\n",
    "# Plot the currently accepted true value\n",
    "ax.axvline(33, color='k', linestyle='--')\n",
    "ax.legend(\n",
    "    (r'posterior of $\\mu$',\n",
    "     r'posterior of $\\mu$ given $y > 0$',\n",
    "     '\"true value\"'),\n",
    "    loc='upper left'\n",
    ")\n",
    "ax.set_title('Normal model')\n",
    "ax.set_xlabel(r'$\\mu$')\n",
    "#ax.set_yticks(())\n",
    "# set bottom to zero\n",
    "ax.set_ylim((0, ax.set_ylim()[1]));"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "bda_py_demos",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
